Physical Sciences and Mathematics Commons^™

Series 06, Ruth Dover

Series

More manipulation of series – substitution, differentiation, and integration.

Alternating Series 1, Ruth Dover

Series

Partial sums of alternating series.

Series 09, Ruth Dover

Series

Practice using series to evaluate limits and definite integrals.

Series 02, Ruth Dover

Series

Repeats Series01 with the function y = arctanx.

2. Geometric Series, Ruth Dover

Series

Quick review of geometric series.

Series 04, Ruth Dover

Series

A closer examination of y = cosx and y = sinx, including error estimation.

Series 01, Ruth Dover

Series

Asks students to create a polynomial function for y = ln(1 + x), extends the polynomial to a series, examines the interval of convergence and error.

Series 03, Ruth Dover

Series

Considers the creation of a general Maclaurin series.

Series 05, Ruth Dover

Series

Popular Maclaurin series and using substitution to create new series.

Approximating Alternating Series, Ruth Dover

Series

Error bounds with alternating series.

4. Integral Test For Series, Ruth Dover

Series

Relating Riemann sums and series – requiring a lot of teacher help!

Taylor Review, Ruth Dover

Series

Assorted problems.

Hidden Symmetries And Commensurability Of 2-Bridge Link Complements, Christian Millichap, William Worden

Faculty Publications

In this paper, we show that any nonarithmetic hyperbolic 2-bridge link complement admits no hidden symmetries. As a corollary, we conclude that a hyperbolic 2-bridge link complement cannot irregularly cover a hyperbolic 3-manifold. By combining this corollary with the work of Boileau and Weidmann, we obtain a characterization of 3-manifolds with nontrivial JSJ-decomposition and rank-two fundamental groups. We also show that the only commensurable hyperbolic 2-bridge link complements are the figure-eight knot complement and the 6²₂ link complement. Our work requires a careful analysis of the tilings of R² that come from lifting the canonical triangulations of …

Compositional Changes For Reduction Of Polymerisation-Induced Shrinkage In Holo, Dervil Cody, Mohesh Moothanchery, Emilia Mihaylova, Vincent Toal, Svetlana Mintova, Izabela Naydenova

Doctoral

Polymerisation-induced shrinkage is one of the main reasons why many photopolymer materials are not used for certain applications including holographic optical elements and holographic data storage. Here, two compositional changes for the reduction of shrinkage in an acrylamide-based photopolymer are reported. A holographic interferometric technique was used to study changes in the dynamics of the shrinkage processes occurring in the modified photopolymer during holographic recording in real time. Firstly, the effect of the replacement of the acrylamide monomer in the photopolymer composition with a larger monomer molecule, diacetone acrylamide, on polymerisation-induced shrinkage has been studied. A reduction in relative shrinkage …

New Facets Of The Balanced Minimal Evolution Polytope, Logan Keefe

Williams Honors College, Honors Research Projects

The balanced minimal evolution (BME) polytope arises from the study of phylogenetic trees in biology. It is a geometric structure which has a variant for each natural number n. The main application of this polytope is that we can use linear programming with it in order to determine the most likely phylogenetic tree for a given genetic data set. In this paper, we explore the geometric and combinatorial structure of the BME polytope. Background information will be covered, highlighting some points from previous research, and a new result on the structure of the BME polytope will be given.

Cluster Algebras And Maximal Green Sequences For Closed Surfaces, Eric Bucher

LSU Doctoral Dissertations

Given a marked surface (S,M) we can add arcs to the surface to create a triangulation, T, of that surface. For each triangulation, T, we can associate a cluster algebra. In this paper we will consider orientable surfaces of genus n with two interior marked points and no boundary component. We will construct a specific triangulation of this surface which yields a quiver. Then in the sense of work by Keller we will produce a maximal green sequence for this quiver. Since all finite mutation type cluster algebras can be associated to a surface, with some rare exceptions, this work …

Growth Conditions For Uniqueness Of Smooth Positive Solutions To An Elliptic Model, Joon Hyuk Kang

Faculty Publications

The uniqueness of positive solution to the elliptic model

∆u + u[a + g(u, v)] = 0 in Ω, ∆v + v[a + h(u, v)] = 0 in Ω, u = v = 0 on ∂Ω,

were investigated.

Understanding The Transition From Secondary Education Mathematics To Undergraduate Mathematics, Amanda D. Stenzelbarton

Dissertations, Master's Theses and Master's Reports

Michigan Technological University had a collective 28% drop, fail, or withdraw rate in four predominantly first-year mathematics classes for the fall semesters from 2011 to 2015, with 58% of students dropping, failing, or withdrawing from College Algebra I in the fall of 2013. A survey was distributed via email to the 2015-2016 first year class of Michigan Tech in an attempt to determine why students struggle in making the transition from high school to undergraduate mathematics class, and what instructors can do to make this transition easier for students. It was found that the time between a student’s last high …

Legalization Of Prostitution And Its Impact On The Market For Human Trafficking, Varunavi Newar

Senior Independent Study Theses

No abstract provided.

Optimal Placement Of Family Planning Centers, Kiera Dobbs

Senior Independent Study Theses

This project investigates and begins to solve the problem of access to family planning services in the United States. We research and implement methods in Operations Research to optimize the location of publicly funded family planning centers in the United States by minimizing travel distance. The solution begins with a designated number of family planning centers for the country. An apportionment integer programming algorithm is then exercised to allocate centers to all the states based on population, percent of population in poverty, and state square mileage. At the state level, we use apportionment again to distribute centers to counties. At …

Mathematical Writing Assignment For Deeper Understanding And Process Writing, Colton Magnant, Saeed Nasseh, Teresa Flateby

Department of Mathematical Sciences Faculty Publications

Brief Description: The broad goals of this writing assignment are two-fold: 1) To delve deeper into the inner workings of a chosen proof and explore fundamental motivation of the chosen result. 2) To enhance student learning in the area of academic writing in the discipline of mathematics.

By walking the students through a process of academic writing, we address the following DQP proficiencies: Specialized Knowledge, Applied and Collaborative Learning and Intellectual Skills - Use of Information Resources, Mathematics-Specific Intellectual and Practical Skills and Communicative Fluency.

Background and context: This assignment has been used in a Mathematical Structures (introduction-to-proofs) course and …

Power Distribution And Probabilistic Forecasting Of Economic Loss And Fatalities Due To Hurricanes, Earthquakes, Tornadoes, And Floods In The United States, Scott Edward Baker

Browse all Theses and Dissertations

Traditionally, the size of natural disaster events such as hurricanes, earthquakes, tornadoes, and floods is measured in terms of wind speed (m/sec), energy released (ergs), or discharge (m3/sec). Economic loss and fatalities from natural disasters result from the intersection of the human infrastructure and population with the natural event. This study investigates the size versus cumulative number distribution of individual natural disaster events in the United States. Economic losses are adjusted for inflation to 2014 United States Dollars (USD). The cumulative number divided by the time over which the data ranges is the basis for making probabilistic forecasts in terms …

My Math Gps: Elementary Algebra Guided Problem Solving (2016 Edition), Jonathan Cornick, G Michael Guy, Karan Puri

Open Educational Resources

My Math GPS: Elementary Algebra Guided Problem Solving is a textbook that aligns to the CUNY Elementary Algebra Learning Objectives that are tested on the CUNY Elementary Algebra Final Exam (CEAFE). This book contextualizes arithmetic skills into Elementary Algebra content using a problem-solving pedagogy. Classroom assessments and online homework are available from the authors.

Junior High School Teachers' Perceptions Of Math Instruction For African American Students, Sandra Denise Richardson

Walden Dissertations and Doctoral Studies

A mathematics achievement gap exists between 8th grade African American students and other ethnic groups. Guided by the conceptual framework of constructivism, the purpose of this case study was to examine 8, Grade 8 math teachers' perceptions of factors contributing to mathematical performance gap in their African American students and what instructional strategies can be used to help reduce the achievement gap in southwest Georgia. Data were obtained through interviews and classroom observations and were coded and analyzed using typological analysis, followed by inductive analysis. The results of the data revealed teachers perceived recruiting and retaining African American teachers and …

Teachers' Perceptions Of Manipulatives During Middle School Math Instruction, Angela L. Vizzi

Walden Dissertations and Doctoral Studies

In a Colorado school district, school personnel and parents were concerned that middle school math proficiency levels were low for 2011-2014 and math teachers were not using manipulatives in their classes to increase math performance. The district's math coordinator did not foresee providing specific professional development (PD) for math manipulative use to address these concerns. Without this PD, math teachers may be ill-quipped to teach math concepts when using manipulatives, which, in turn, could lead to further poor math performance. The purpose of this qualitative bounded collective case study was to explore middle school teachers' perceptions of PD and perceived …

Understanding The Relationships Among Students' Goal Orientations, Self-Efficacy, Anxiety, And Accelerated Academic Success In The Redesign Of Developmental Mathematics, Kelly Ann Hogan

Walden Dissertations and Doctoral Studies

The low success rates of increasing numbers of underprepared students taking developmental mathematics classes 'often minority and economically disadvantaged' are challenging community colleges across the United States. These students, who must start in the lowest levels of precollege mathematics courses, are unlikely to pass the first course and earn a credential. Using a mastery goal orientation theoretical framework, a quantitative, survey research design was used to ascertain any correlations between students' goal orientations, self-efficacy, test anxiety, and success in a new model of learning. Survey data were used to answer 3 research questions: (a) the relationship between success and students' …

A Quantitative Quasi-Experimental Study Of An Online High School Mathematics Remediation Program, Terry Meehan

Walden Dissertations and Doctoral Studies

The local problem that drove this study is that a high school in an upper middle class suburban city in Pennsylvania wants to improve its student scores on its end-of-course Algebra 1 Keystone Exam. The purpose of this study was to conduct a quantitative, quasi-experimental assessment of an online high school mathematics remediation program to determine if the remediation program was successful in its endeavor to remediate students. This research study, informed by the self-efficacy and the behaviorist learning theories, attempted to determine whether students who (a) scored below proficient on the May algebra exam and were placed in the …

Follower And Extender Sets In Symbolic Dynamics, Thomas Kelly French

Electronic Theses and Dissertations

Given a word w in the language of a one-dimensional shift space X, the follower set of w, denoted F_X(w), is the set of all right-infinite sequences which follow w in some point of X. Extender sets are a generalization of follower sets and are defined similarly. To a given shift space X, then, we may associate a follower set sequence {|F_X(n)|} which records the number of distinct follower sets in X corresponding to words of length n. Similarly, we may define an extender set sequence {|E …

Using Mathematical Research Methods To Solve A Problem In Music Theory Instruction, Specifically, The Teaching Of Secondary Dominant Chords, Angela Ulrich

Williams Honors College, Honors Research Projects

The mathematical method for research is used to find a solution to a problem in music theory: understanding and identifying secondary dominant chords. By reviewing and assessing the teaching methods of university professors and theory textbooks, and comparing those findings with student reviews, a new method for teaching the concept is developed. The proposed system incorporates aural, visual, and kinetic exercises to serve every learner. The literature review and sample unit plan are followed by a possible procedure for testing the effectiveness of the new method.

Subgroups Of Finite Wreath Product Groups For P=3, Jessica L. Gonda

Williams Honors College, Honors Research Projects

Let M be the additive abelian group of 3-by-3 matrices whose entries are from the ring of integers modulo 9. The problem of determining all the normal subgroups of the regular wreath product group P=Z₉≀(Z₃ × Z₃) that are contained in its base subgroup is equivalent to the problem of determining the subgroups of M that are invariant under two particular endomorphisms of M. In this thesis we give a partial solution to the latter problem by implementing a systematic approach using concepts from group theory and linear algebra.